RT Journal Article
T1 Computational and analytical studies of the Randic index in Erdös-Rényi models
A1 Martínez-Martínez, C. T.
A1 Méndez-Bermúdez, J. A.
A1 Rodríguez García, José Manuel
A1 Sigarreta Almira, José María
AB In this work we perform computational and analytical studies of the Randic´ index R(G) in Erdös–Rényi models G(n, p) characterized by n vertices connected independently with probability p ∈ (0, 1). First, from a detailed scaling analysis, we show that R(G) = {R(G)}/(n/2) scales with the product ξ ≈ np, so we can define three regimes: a regime of mostly isolated vertices when ξ < 0.01 (R(G) ≈ 0), a transition regime for 0.01 < ξ < 10 (where 0 < R(G) < n/2), and a regime of almost complete graphs for ξ > 10 (R(G) ≈ n/2). Then, motivated by the scaling of R(G), we analytically (i) obtain new relations connecting R(G) with other topological indices and characterize graphs which are extremal with respect to the relations obtained and (ii) apply these results in order to obtain inequalities on R(G) for graphs in Erdös–Rényi models.
PB Elsevier
SN 0096-3003
YR 2020
FD 2020-07-15
LK https://hdl.handle.net/10016/38284
UL https://hdl.handle.net/10016/38284
LA eng
NO J.A.M.-B. acknowledges financial support from FAPESP (Grant No. 2019/06931-2), Brazil, and PRODEP-SEP (Grant No. 511- 6/2019.-11821), Mexico. J.M.R. and J.M.S. were supported in part by two grants from Ministerio de Economía y Competitividad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain.
DS e-Archivo
RD 17 jul. 2024